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Comparison of Bootstrap Methods for Estimating Causality in Linear Dynamic Systems: A Review.

Fumikazu Miwakeichi1,2, Andreas Galka3

  • 1Department of Statistical Modeling, The Institute of Statistical Mathematics, Tokyo 190-8562, Japan.

Entropy (Basel, Switzerland)
|July 29, 2023
PubMed
Summary

The AutoRegressive-Sieve Bootstrap (ARSB) method is superior for time series causal analysis, accurately detecting feedback and causality in all variables. Other bootstrap methods showed limitations in identifying self-feedback and causality.

Keywords:
Granger causalitybootstrap methodscausal analysisimpulse response functionmultivariate time series

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Area of Science:

  • Time Series Analysis
  • Causal Inference
  • Statistical Modeling

Background:

  • Assessing causality in time series data is crucial for understanding complex systems.
  • Various bootstrap methods exist for significance testing, but their performance in causal analysis varies.
  • Accurate detection of feedback loops and causal relationships is essential for reliable analysis.

Purpose of the Study:

  • To comprehensively compare the performance of four distinct bootstrap methods for causal analysis in time series.
  • To evaluate the effectiveness of uncorrelated Phase Randomization Bootstrap (uPRB), Time Shift Bootstrap (TSB), Stationary Bootstrap (SB), and AutoRegressive-Sieve Bootstrap (ARSB).
  • To identify the most reliable method for detecting self-feedback and causality in multivariate time series data.

Main Methods:

  • Generated multivariate simulated data from a linear feedback system.
  • Investigated four bootstrap methods: uPRB, TSB, SB, and ARSB.
  • Analyzed the performance of each method in detecting variable interactions, self-feedback, and causality, including Impulse Response Function (IRF) analysis.

Main Results:

  • uPRB accurately identified variable interactions but missed some self-feedback.
  • TSB performed worse than uPRB and failed to detect certain feedback.
  • SB provided consistent results but decreased self-feedback detection with increasing block width.
  • ARSB demonstrated superior performance, accurately detecting both self-feedback and causality across all variables and in IRF analysis.

Conclusions:

  • The AutoRegressive-Sieve Bootstrap (ARSB) method is the most effective for causal analysis in time series data.
  • ARSB accurately captures both self-feedback and causality, outperforming uPRB, TSB, and SB.
  • The choice of bootstrap method significantly impacts the reliability of causal inference in time series analysis.